Not interested in having a big argument about this, so I'm just gonna state the facts. You can do whatever you want with them.
Consider that there is nothing that becomes visible through this remote device check that could be used to identify you, personally. The unique ESN/MEID/Device ID is already in their billing system along with its usage and update history. All of this information is, in my opinion, much more unique than what is gained through the remote software.
Just because one has a sense of possession about something and desires that its information be kept to one's self doesn't mean it's defensible by privacy law. You might feel that this information *should* be private, but it is simply not defined as such by law. Complain about the ethics or morality if you wish, but it is not currently recognized as illegal.
Information Collected When You Use Verizon Products and Services:
We collect information about your use of our products, services and sites. Information such as call records, websites visited, wireless location, application and feature usage, network traffic data, product and device-specific information, service options you choose, mobile and device numbers, video streaming and video packages and usage, movie rental and purchase data, FiOS TV viewership, and other similar information may be used for billing purposes, to deliver and maintain products and services, or to help you with service-related issues or questions. In addition, this information may be used for purposes such as providing you with information about product or service enhancements, determining your eligibility for new products and services, and marketing to you based on your use of your products and services. This information may also be used to manage and protect our networks, services and users from fraudulent, abusive, or unlawful uses; and help us improve our services, research and develop new products, and offer promotions and other services.